X, Y and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work ?

A. 12

B. 16

C. 24

D. 36

Answer: Option C

Solution(By Examveda Team)

(X + Y)'s 1 day's work
$$\eqalign{ & = \left( {\frac{1}{{16}} + \frac{1}{{16}}} \right) \cr & = \frac{2}{{16}} \cr & = \frac{1}{8} \cr} $$
∴ Z's 1 day's work
(X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
$$\eqalign{ & = \frac{1}{6} - \frac{1}{8} \cr & = \frac{1}{{24}} \cr} $$
∴ Z alone can finish the work in 24 days.